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Sequential Estimation of Structural Models with a Fixed Point Constraint

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  • Kasahara, Hiroyuki
  • Shimotsu, Katsumi

Abstract

This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a fixed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze the conditions under which the nested pseudo-likelihood (NPL) algorithm converges to a consistent estimator and derive its convergence rate. We find that the NPL algorithm may not necessarily converge to a consistent estimator when the fixed point mapping does not have a local contraction property. To address the issue of divergence, we propose alternative sequential estimation procedures that can converge to a consistent estimator even when the NPL algorithm does not.

Suggested Citation

  • Kasahara, Hiroyuki & Shimotsu, Katsumi, 2009. "Sequential Estimation of Structural Models with a Fixed Point Constraint," Discussion Papers 2009-18, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2009-18
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    References listed on IDEAS

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    1. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
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    5. Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices," Working Papers 1092, Queen's University, Department of Economics.
    6. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
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    12. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    13. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
    14. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.
    15. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
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    Cited by:

    1. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
    2. Jinhyuk Lee & Kyoungwon Seo, 2015. "A computationally fast estimator for random coefficients logit demand models using aggregate data," RAND Journal of Economics, RAND Corporation, vol. 46(1), pages 86-102, March.
    3. Aguirregabiria, Victor & Ho, Chun-Yu, 2012. "A dynamic oligopoly game of the US airline industry: Estimation and policy experiments," Journal of Econometrics, Elsevier, vol. 168(1), pages 156-173.
    4. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2014. "Testing Equilibrium Multiplicity in Dynamic Games," CEPR Discussion Papers 10111, C.E.P.R. Discussion Papers.
    5. repec:eee:ecolet:v:161:y:2017:i:c:p:86-89 is not listed on IDEAS
    6. Sumon Datta & K. Sudhir, 2012. "Does Reducing Spatial Differentiation Increase Product Differentiation? Effects of Zoning on Retail Entry and Format Variety," Cowles Foundation Discussion Papers 1851, Cowles Foundation for Research in Economics, Yale University, revised Sep 2012.
    7. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Apr 2018.
    8. José-Alberto Guerra & Myra Mohnen, 2017. "Multinomial choice with social interactions: occupations in Victorian London," DOCUMENTOS CEDE 015667, UNIVERSIDAD DE LOS ANDES-CEDE.
    9. Taisuke Otsu & Martin Pesendorfer & Yuya Takahashi, 2016. "Pooling data across markets in dynamic Markov games," Quantitative Economics, Econometric Society, vol. 7(2), pages 523-559, July.
    10. Fabio A. Miessi Sanches & Daniel Silva Junior, Sorawoot Srisuma, 2014. "Ordinary Least Squares Estimation for a Dynamic Game," Working Papers, Department of Economics 2014_19, University of São Paulo (FEA-USP), revised 23 Feb 2015.
    11. Otero, Karina V., 2016. "Nonparametric identification of dynamic multinomial choice games: unknown payoffs and shocks without interchangeability," MPRA Paper 86784, University Library of Munich, Germany.

    More about this item

    Keywords

    contraction; dynamic games; nested pseudo likelihood; recursive projection method;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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